So what about Cantor?s much celebrated non-denumerable real? Where isit? Did Cantor produce such a real number? No, he merely sketched outthe logic for a nonterminal procedure that would produce an infinitelylong digit string representing a real number that would not be in theinput stream of enumerated reals. Cantor?s procedure, and with it hiscelebrated nondenumerable, infinitely long real number, will appearwith 100% certainty in the denumerable list of procedures. {{That'sthe point: Every diagonal number can be distinguished at a finiteposition from every other number. But if all strings are there to anyfinite dephts, as is easily visualized in the Binary Tree, then thereis no chance for distinction at a finite position - and otherpositions are not available.}} There is no non-denumerable real, and every source of real numbersis denumerable [...] Implications throughout mathematics that buildupon Cantor?s Diagonal Proof must now be carefully reconsidered. So Who Won? Professor Leopold Kronecker was right. Irrationals arenot real {{ - at least they have no real strings of digits, and onlycountably many of them can be defined in a language that can bespoken, learned and understood}}. God made all the integers and Manmade all the rest {{and in addition something more - unfortunately.}}[Brian L. Crissey: "Kronecker 1, Cantor 0: The End of a Hundred Years?War"]http://www.briancrissey.info/files/Kronecker1Cantor0.pdf